I don't believe your system is functioning correctly. Specifically, your compressor should not be shutting off while idling at a light simply because you hit the gas a little. The only systems that I'm familiar with like you mentioned are ones that turn off the a/c compressor when the TPS recognizes WOT. I'd test the load on your compressor and make sure it's not being overworked, these are not cheap parts to replace. You can use this
auto forum search engine for more information as odds are it's a slightly complicated issue. At least you are still getting cold air.